PCA dimensionality Reduction--a view of the maximum variance

PCA reduction by the maximum variance method (Welcome discussion)

On the basis of the previous article, we will continue to discuss:

First, the center point of the original space is obtained:

Assuming that U1 is a projection vector, the variance after the projection is:

The variance is the largest (i.e., the points after the projection are scattered and have no correlation.) To achieve a good dimensionality reduction effect), using Lagrange multiplier method, u1t u1=1 as the constraint condition.

Then the variance expression for UT can be written as:

The derivative of the above to UT, so that it is 0, to obtain:

In this way, the problem of finding eigenvalues and eigenvectors of linear algebra is obtained.

PCA dimensionality Reduction--a view of the maximum variance